Songtree

Should I ask permission to overdub a song?

No - but you can if you want to. The idea behind Songtree is to be an open collaborative platform, where any user can overdub any song by any other user. If an overdub turns out to be not so great, that's not a problem for the author(s) of the original songs. Having one of your songs overdubbed increases the prestige (badge score) of the original song owner so even if one doesn't like an overdub he/she should still be happy because it means that his/her song was chosen because it was good or interesting and deserved to be overdubbed (bad songs rarely get overdubbed). Also an overdub doesn't in any way alter the original song, which continues to remain open for listening and for other overdubs.
If you don't want your songs to be overdubbed at all you can set your song to be "locked" (using the lock icon on the song on your profile page), which prohibits any user from overdubbing the song.